Positive solutions for m-point p-Laplacian fractional boundary value problem involving Riemann Liouville fractional integral boundary conditions on the half line

Oz, Dondu; Karaca, Ilkay Yaslan

doi:10.2298/fil2009161o

Cited by 5 publications

(2 citation statements)

References 27 publications

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“…Most articles and books on fractional calculus in the setting of special functions concentrate on the solvability of linear fractional differential equations [5][6][7][8][9][10][11][12][13]. Several new papers dealing with nonlinear fractional differential equations and their solutions using methods such as the stability analysis, Leray-Schauder theorem, and fixed point analysis have recently been published [14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

On the novel existence results of solutions for a class of fractional boundary value problems on the cyclohexane graph

2022

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A branch of mathematical science known as chemical graph theory investigates the implications of connectedness in chemical networks. A few researchers have looked at the solutions of fractional differential equations using the concept of star graphs. Their decision to use star graphs was based on the assumption that their method requires a common point linked to other nodes but not to each other. Our goal is to broaden the scope of the method by defining the idea of a cyclohexane graph, which is a cycloalkane with the molecular formula $C_{6}H_{12}$ C 6 H 12 and CAS number 110-82-7. It consists of a ring of six carbon atoms, each bonded with two hydrogen atoms above and below the plane with multiple junction nodes. This article examines the existence of fractional boundary value problem’ solutions on such graphs in the sense of the Caputo fractional derivative by using the well-known fixed point theorems. In addition, an example is given to support our key findings.

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Section: Introductionmentioning

confidence: 99%

On the novel existence results of solutions for a class of fractional boundary value problems on the cyclohexane graph

2022

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“…Fractional calculus has been studied by many mathematicians and physicists for applications in potential theory, physics, electro-chemistry, biophysics, viscoelasticity, biomedicine, control theory, and signal processing (see other studies [1][2][3][4] and the references therein). We refer the reader to Podlubny for the history of FDEs (see Podlubny 5 ).…”

Section: Introductionmentioning

confidence: 99%

Stability of fractional order of time nonlinear fractional diffusion equation with Riemann–Liouville derivative

Long

Binh

Kumar

et al. 2022

Math Methods in App Sciences

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In this paper, we investigate an equation of nonlinear fractional diffusion with the derivative of Riemann-Liouville. Firstly, we determine the global existence and uniqueness of the mild solution. Next, under some assumptions on the input data, we discuss continuity with regard to the fractional derivative order for the time. Our key idea is to combine the theories Mittag-Leffler functions and Banach fixed-point theorem. Finally, we present some examples to test the proposed theory.

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Positive solutions for a class of fractional differential equations with infinite-point boundary conditions on infinite intervals

Cui,

Zhou

2023

Bound Value Probl

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In this paper, the existence of the multiple positive solutions for a class of higher-order fractional differential equations on infinite intervals with infinite-point boundary value conditions is mainly studied. First, we construct the Green function and analyze its properties, and then by using the Leggett–Williams fixed point theorem, some new results on the existence of positive solutions for the boundary value problem are obtained. Finally, we illustrate the application of our conclusion by an example.

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Positive solutions for m-point p-Laplacian fractional boundary value problem involving Riemann Liouville fractional integral boundary conditions on the half line

Cited by 5 publications

References 27 publications

On the novel existence results of solutions for a class of fractional boundary value problems on the cyclohexane graph

On the novel existence results of solutions for a class of fractional boundary value problems on the cyclohexane graph

Stability of fractional order of time nonlinear fractional diffusion equation with Riemann–Liouville derivative

Positive solutions for a class of fractional differential equations with infinite-point boundary conditions on infinite intervals

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